Lévy-driven Polling Systems and Continuous-State Branching Processes

References

• J. Abate and W. Whitt. Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comp., 7:36–43, 1995.Link, Google Scholar
• J. Abate and W. Whitt. A unified framework for numerically inverting Laplace transforms. INFORMS J. Comput., 18:408–421, 2006. MR2274708Link, Google Scholar
• E. Altman. Stochastic recursive equations with applications to queues with dependent vacations. Annals of Operations Research, 112:43–61, 2002. MR1960670Google Scholar
• E. Altman and D. Fiems. Expected waiting time in symmetric polling systems with correlated walking times. Queueing Syst., 56:241–253, 2007. MR2336110Google Scholar
• S. Asmussen. Applied Probability and Queues. Springer, 2nd edition, 2002. MR1978607Google Scholar
• O.J. Boxma. Workloads and waiting times in single-server systems with multiple customer classes. Queueing Syst., 5:185–214, 1989. MR1032554Google Scholar
• O.J. Boxma. Polling systems. In K. Apt, A. Schrijver, and N. Temme, editors, Liber Amicorum for P.C. Baayen., pages 215–230. CWI, Amsterdam, 1994. MR1490592Google Scholar
• O.J. Boxma, H. Levy, and U. Yechiali. Cyclic reservation schemes for efficient operation of multiple-queue single-server systems. Ann. Oper. Res., 35:187–208, 1992.Google Scholar
• O.J. Boxma, Q. Deng, and J.A.C. Resing. Polling systems with regularly varying service and/or switchover times. Adv. Perf. Anal., 3:71–107, 2000.Google Scholar
• O.J. Boxma, M. Mandjes, and O. Kella. On a queueing model with service interruptions. Probab. Engrg. Infor. Sci., 22:537–555, 2008. MR2452336Google Scholar
• G.L. Choudhury and W. Whitt. Computing distributions and moments in polling models by numerical transform inversion. Performance Evaluation, 25:267–292, 1996.Google Scholar
• O. Czerniak and U. Yechiali. Fluid polling systems. Queueing Syst., 63:401–435, 2009. MR2576020Google Scholar
• I. Eliazar. Gated polling systems with Lévy inflow and inter-dependent switchover times: a dynamical systems approach. Queueing Syst., 49:49–72, 2005. MR2119657Google Scholar
• S.W. Fuhrmann. Performance analysis of a class of cyclic schedules. Technical Report 81-59531-1., Bell Laboratories, 1981.Google Scholar
• S.W. Fuhrmann. A decomposition result for a class of polling models. Queueing Syst., 11:109–120, 1992. MR1178645Google Scholar
• M. Jiřina. Stochastic branching processes with continuous state space. Czechosl. Math. J., 8:292–313, 1958. MR0101554Google Scholar
• O. Kella and W. Whitt. Useful martingales for stochastic storage processes with Lévy input. J. Appl. Probab., 29:396–403, 1992. MR1165224Google Scholar
• A.E. Kyprianou. Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer-Verlag, Berlin Heidelberg, 2006. MR2250061Google Scholar
• H. Levy and M. Sidi. Polling systems with correlated arrivals. In Technology: Emerging or Converging, IEEE, volume 3 of Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies, pages 907–913. INFOCOM ’89, 1989.Google Scholar
• H. Levy and M. Sidi. Polling models: applications, modeling and optimization. IEEE Trans. Commun., 38:1750–1760, 1990.Google Scholar
• A.G. Pakes. Some limit theorems for Jiřina processes. Period. Math. Hungar., 1:55–66, 1979. MR0494544Google Scholar
• N.U. Prabhu. Stochastic Storage Processes: Queues, Insurance Risk, Dams, and Data Communication. Springer-Verlag, New York, 2nd edition, 1998. MR1492990Google Scholar
• J.A.C. Resing. Polling systems and multitype branching processes. Queueing Syst., 13:409–426, 1993. MR1231052Google Scholar
• K. Sato. Lévy Processes and Infinitely Divisible Distributions, volume 68 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1999. MR1739520Google Scholar
• E. Seneta. Non-negative Matrices and Markov Chains. Springer-Verlag, New York, 2nd edition, 1981. MR2209438Google Scholar
• E. Seneta and D. Vere-Jones. On the asymptotic behaviour of subcritical branching processes with continuous state space. Z. Wahrscheinlichkeitstheorie verw. Geb., 10: 212–225, 1968. MR0239667Google Scholar
• E. Seneta and D. Vere-Jones. On a problem of M. Jiřina concerning continuous state branching processes. Czechosl. Math. J., 19:277–283, 1969. MR0246379Google Scholar
• H. Takagi. Queueing Analysis, volume 1. North-Holland, Amsterdam, 1991. MR1149382Google Scholar
• H. Takagi. Application of polling models to computer networks. Comput. Netw. ISDN Syst., 22:193–211, 1991.Google Scholar
• H. Takagi. Analysis and application of polling models. In G. Haring, C. Lindemann, and M. Reiser, editors, Performance Evaluation: Origins and Directions, volume 1769 of Lecture Notes in Computer Science, pages 423–442. Springer, Berlin, 2000.Google Scholar
• V.M. Vishnevskii and O.V. Semenove. Mathematical methods to study the polling systems. Autom. Remote Control, 67:173–220, 2006. MR2210457Google Scholar
• W. Whitt. Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer-Verlag, 2002. MR1876437Google Scholar